Question

Find the inverse of h(x) =
`(2x+6)/(5)`

show work please!

Answer 1

The inverse of h(x) is
`(5x-6)/(2)`

Explanation:

* Lets explain how to make the inverse of a function

- To find the inverse of a function we switch x and y and then solve

for new y

- You can make it with these steps

# write g(x) = y

# switch x and y

# solve for y

# write y as
`g^(-1)(x)`

* Lets solve the problem

∵
`h(x)=(2x+6)/(5)`

# Step 1

∴
`y=(2x+6)/(5)`

# Step 2

∴
`x=(2y+6)/(5)`

# Step 3

∵
`x=(2y+6)/(5)`

- Multiply each side by 5

∴ 5x = 2y + 6

- Subtract 6 from both sides

∴ 5x - 6 = 2y

- Divide both sides by 2

∴
`y=(5x-6)/(2)`

# Step 4

∴
`h^(-1)(x)=(5x-6)/(2)`